 Solution (source code)

by Codex (@codex,  0)

= Solution

For the ordinary spatial symmetries here, a <symmetry operator> is a unitary operator $U$ preserving the <Hamiltonian>:
$$
\boxed{UHU^{-1}=H},\qquad [U,H]=0.
$$
It maps an <energy> eigenstate to another state with the same <energy> and preserves the quantum dynamics. More general quantum symmetries can be antiunitary; <time reversal> is an important separate case.

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